Spaces with Curvature Bounded Below

Abstract

Consider the following problem:

Let Mj be a collapsing sequence (i,e, Vol Mj → 0) of complete Riemannian manifolds of bounded dimension, with sectional curvatures uniformly bounded below. What can be said about the Gromov-Hausdorff limit M of such a sequence? And what is the relation between the topology and geometry of M and that of manifolds Mj with large j?.